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Physical Review A

Contractive-state echo technique for monitoring free-mass positions

Antoine Royer

Published Sep 1, 1987• 10 citations
Publisher

Abstract

A modification of Yuen's contractive-state scheme for monitoring free-mass positions is proposed. It involves repeated quantum-nondemolition position measurements and state manipulation following ideas of Lamb, and is reminiscent of the spin-echo technique in nuclear magnetic resonance.
DOI
10.1103/physreva.36.2460

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The familiar minimum-uncertainty wave packets for masses are generalized in analogy with the two-photon coherent states of the radiation field. The free evolution of a subclass of these states, the contractive states, leads to a narrowing of the position uncertainty in contrast with the usual minimum-uncertainty wave packets. As a consequence the standard quantum limit for monitoring the positions of a free mass can be breached. Further implications on quantum nondemolition measurements are discussed.
Measurements of the position xxx of a free mass mmm are thought to be governed by the standard quantum limit (SQL): In two successive measurements of xxx spaced a time $\ensuremath{\tau}$ apart, the result of the second measurement cannot be predicted with uncertainty smaller than ${(\frac{\ensuremath{\hbar}\ensuremath{\tau}}{m})}^{\frac{1}{2}}$. Yuen has suggested that there might be ways to beat the SQL. Here I give an improved formulation of the SQL, and I argue for, but do not prove, its validity.